KR102669448B1 - Method for mitigating an error of quantum circuit and apparatus thereof - Google Patents

Abstract

The present invention relates to a quantum circuit error correction method in a quantum computer, comprising: detecting a quantum circuit to be corrected among a plurality of quantum circuits constituting the quantum computer; calling a pre-trained deep learning model to correct errors in the plurality of quantum circuits; inferring an error correction value of the detected quantum circuit using the called deep learning model; and correcting the detected error of the quantum circuit based on the inferred error correction value.

Description

Quantum circuit error correction method and device {METHOD FOR MITIGATING AN ERROR OF QUANTUM CIRCUIT AND APPARATUS THEREOF}

The present invention relates to quantum computer technology, and more specifically, to a method and device that can correct (reduce) errors existing in quantum circuits that make up a quantum computer.

A quantum computer is a new concept of computer that can simultaneously process multiple pieces of information using the unique physical characteristics of quantum, such as superposition and entanglement. The need for quantum computers is growing as an alternative to overcome the performance limitations of classical computers due to leakage currents generated in the microcircuits of modern semiconductor chips. Quantum computers use quantum bits, or qubits, which are quantum information units, as the basic unit of information processing, and the speed of information processing and calculation increases exponentially, solving problems at high speed. You can. Accordingly, quantum computers are expected to bring about great innovation in various industries such as finance, chemistry, and pharmaceuticals, as they have strengths in complex calculations and mass data processing such as optimal path search, prime factorization, and mass data search.

The major element technologies that make up a quantum computer include qubit implementation technology, quantum algorithm technology, quantum error correction code (QECC) technology, and quantum circuit technology. Among these element technologies, quantum circuit technology includes technology that implements a quantum gate for information processing of qubits, a unit of quantum information, and technology that eliminates errors existing in quantum circuits. A representative technology for removing errors existing in the quantum circuit is quantum circuit error correction (QEC) technology.

Basically, errors that exist in a quantum circuit consist of errors depending on the types of quantum gates that make up the circuit and errors depending on the order of combination of the quantum gates. In other words, the error that exists in a quantum circuit depends not only on the configuration of the quantum gates but also on the order of combination of the quantum gates. Therefore, the conventional quantum circuit error correction (QEC) technology corrects errors existing in the circuit by considering the types and orders of quantum gates that make up the quantum circuit. However, this quantum circuit error correction (QEC) technology not only requires a separate quantum circuit, but the computational process for error correction is very complicated, so a significant amount of time and energy is consumed to correct errors existing in the quantum circuit. there is.

The present invention aims to solve the above-mentioned problems and other problems. Another purpose is to provide a quantum circuit error correction method and device that can effectively correct (reduce) errors existing in a quantum circuit using a pre-trained deep learning model.

In order to achieve the above or other objects, according to one aspect of the present invention, the steps include: detecting a quantum circuit to be corrected among a plurality of quantum circuits constituting a quantum computer; calling a pre-trained deep learning model to correct errors in the plurality of quantum circuits; inferring an error correction value of the detected quantum circuit using the called deep learning model; and correcting an error in the detected quantum circuit based on the inferred error correction value.

According to another aspect of the present invention, a memory that stores a deep learning model learned in advance for error correction of a plurality of quantum circuits constituting a quantum computer; and detecting a quantum circuit to be corrected among the plurality of quantum circuits, inferring an error correction value of the detected quantum circuit using a deep learning model stored in the memory, and based on the inferred error correction value. Provided is a quantum circuit error correction device including a processor that corrects errors in the detected quantum circuit.

According to another aspect of the present invention, a process of detecting a quantum circuit to be corrected among a plurality of quantum circuits constituting a quantum computer; A process of calling a pre-trained deep learning model to correct errors in the plurality of quantum circuits; A process of inferring an error correction value of the detected quantum circuit using the called deep learning model; and a computer program stored in a computer-readable recording medium so that a process of correcting the detected error of the quantum circuit based on the inferred error correction value can be executed on a computer.

The effects of the quantum circuit error correction method and device according to embodiments of the present invention will be described as follows.

According to at least one of the embodiments of the present invention, errors existing in a quantum circuit are easily corrected using a pre-trained deep learning model, so not only is there no need to separately add quantum gates to correct quantum circuit errors, The computational process for quantum circuit error correction is simple, which has the advantage of saving the time and energy required to correct errors existing in the quantum circuit.

However, the effects that can be achieved by the quantum circuit error correction method and device according to the embodiments of the present invention are not limited to those mentioned above, and other effects not mentioned can be found in the technology to which the present invention belongs from the description below. It will be clearly understandable to those with ordinary knowledge in the field.

1A is a diagram showing the basic structure of a deep neural network (DNN) related to the present invention;
1B is a diagram referenced to explain the learning process of a deep neural network (DNN) related to the present invention;
2A is a diagram showing the basic structure of a convolutional neural network (CNN) related to the present invention;
Figure 2b is a diagram referenced to explain the learning process of a convolutional neural network (CNN) related to the present invention;
Figure 3 is a diagram illustrating types of quantum gates relevant to the present invention;
FIG. 4 is a diagram showing an example of a quantum circuit constructed using the quantum gates of FIG. 3;
Figure 5 is a diagram schematically showing the structure of a quantum circuit related to the present invention;
Figure 6 is a flow chart illustrating a quantum circuit error correction method according to an embodiment of the present invention;
Figure 7 is a diagram showing the structure of a DNN model according to an embodiment of the present invention;
Figure 8 is a diagram showing the structure of a DNN model according to another embodiment of the present invention;
Figure 9 is a diagram referenced to explain data input to the input layer of the DNN model;
Figure 10 is a diagram referenced to explain the process of selecting a learning target quantum circuit and learning a DNN model based on the selected learning target quantum circuit;
FIG. 11 is a diagram referenced to explain the types of quantum circuits to be corrected and the process of correcting errors in the quantum circuits to be corrected using a previously learned DNN model;
12A and 12B are diagrams referenced to explain the structure of an H-CNN model and learning data input to the input layer and output layer of the model according to an embodiment of the present invention;
Figure 13 is a diagram referenced to explain the process of selecting a learning target quantum circuit and learning an H-CNN model based on the selected learning target quantum circuit;
FIG. 14 is a diagram referenced to explain the type of quantum circuit to be corrected and the process of correcting errors in the quantum circuit to be corrected using a pre-learned H-CNN model;
15 is a block diagram of a computing device according to an embodiment of the present invention.

Hereinafter, embodiments disclosed in the present specification will be described in detail with reference to the attached drawings. However, identical or similar components will be assigned the same reference numbers regardless of reference numerals, and duplicate descriptions thereof will be omitted. The suffixes “module” and “part” for components used in the following description are given or used interchangeably only for the ease of preparing the specification, and do not have distinct meanings or roles in themselves. That is, the term 'unit' used in the present invention refers to a hardware component such as software, FPGA, or ASIC, and the 'unit' performs certain roles. However, 'wealth' is not limited to software or hardware. The 'part' may be configured to reside on an addressable storage medium and may be configured to run on one or more processors. Therefore, as an example, 'part' refers to components such as software components, object-oriented software components, class components and task components, processes, functions, properties, procedures, Includes subroutines, segments of program code, drivers, firmware, microcode, circuits, data, databases, data structures, tables, arrays, and variables. The functionality provided within the components and 'parts' may be combined into a smaller number of components and 'parts' or may be further separated into additional components and 'parts'.

Additionally, in describing the embodiments disclosed in this specification, if it is determined that detailed descriptions of related known technologies may obscure the gist of the embodiments disclosed in this specification, the detailed descriptions will be omitted. In addition, the attached drawings are only for easy understanding of the embodiments disclosed in this specification, and the technical idea disclosed in this specification is not limited by the attached drawings, and all changes included in the spirit and technical scope of the present invention are not limited. , should be understood to include equivalents or substitutes.

The present invention proposes a quantum circuit error correction method and device that can effectively correct (or reduce) errors existing in a quantum circuit using a pre-trained deep learning model. The deep learning model may be a deep neural network (DNN) or a hybrid convolutional neural network (H-CNN), but is not necessarily limited thereto.

Hereinafter, various embodiments of the present invention will be described in detail with reference to the drawings.

FIG. 1A is a diagram showing the basic structure of a deep neural network (DNN) related to the present invention, and FIG. 1B is a diagram referenced to explain the learning process of the deep neural network (DNN) shown in FIG. 1A.

Referring to FIGS. 1A and 1B, the multi-layer perceptron (MLP, 100) related to the present invention is the most basic structure of a deep neural network (DNN), and includes an input layer (110) and a hidden layer (hidden layer). It consists of a layer 120) and an output layer 130.

The multilayer perceptron 100 is an artificial neural network structure proposed to overcome the limitations of a single perceptron. In other words, the multi-layer perceptron 100 is an artificial neural network structure proposed to enable learning even on non-linearly separated data, such as an XOR gate (exclusive-OR gate). To this end, the multi-layer perceptron 100, unlike the single perceptron, has a structure that further includes one or more hidden layers 120.

The input layer 110 of the multi-layer perceptron 100 refers to the layer where the input vector corresponding to the learning data is located, and the output layer 130 refers to the layer where the final result of the learning model is located. And, the hidden layer 120 refers to all layers existing between the input layer 110 and the output layer 130. As the number of hidden layers 120 increases, the artificial neural network is called ‘deeper’, and a sufficiently deep artificial neural network is called a deep neural network (DNN).

In this multi-layer perceptron structure, the nodes existing in the input layer 110 do not use parameters and activation functions, while the nodes existing in the hidden layer 120 and the output layer 130 use parameters. and use the activation function. Here, the parameter is a value that changes automatically through a learning process and may include weight and bias. Weight is a parameter that controls the degree of influence that an input signal has on the resulting output, and bias is a parameter that controls how easily a node (or neuron) is activated. An activation function refers to a function that receives a signal as input, processes it appropriately, and outputs it. As the activation function, a sigmoid function, a Rectified Linear Unit (ReLU) function, a softmax function, an identity function, etc. may be used, but are not necessarily limited thereto.

The multi-layer perceptron 100 has a fully-connected structure in which nodes (i.e., neurons, nodes) of each layer are connected two-dimensionally. At this time, the fully connected structure is a structure in which a connection relationship does not exist between nodes located on the same layer, and a connection relationship exists only between nodes located on an immediately adjacent layer.

The learning operation of this multi-layer perceptron 100 is briefly explained as follows. First, set the initial values of the weight and bias parameters in each layer. Afterwards, the net input function value in each layer is calculated for one learning (training) data, and finally the output value (i.e., result value) by the activation function is calculated. Here, the net input function value refers to the value input to the activation function of each node. Next, the weights and biases in each layer are updated so that the difference between the output value by the activation function of the output layer and the actual value is within the tolerance. Finally, for all learning data, learning is terminated when the difference between the output value by the activation function of the output layer and the actual value is within the tolerance.

For example, as shown in FIG. 1B, the learning process of the multi-layer perceptron 100 can be defined as an iterative process of feedforward (FF) and backpropagation (BP). This repetitive process may continue until the difference (i.e., error) between the result calculated by the output layer 130 and the actual value approaches 0.

In the forward propagation (FF) process, the weight (w) corresponding to each input is multiplied while moving from the input layer 110 to the output layer 130, and as a result, the weight sum is calculated and input into the activation function of each layer, It refers to a series of learning processes in which results are finally output from the activation function of the output layer 130.

The back propagation (BP) process refers to a series of learning processes that update the weights and biases of each layer to reduce errors generated during the forward propagation process while moving from the output layer 130 to the input layer 110. Gradient descent may be used as a method for determining weights in the back propagation (BP) process, but is not necessarily limited thereto.

Gradient descent is an optimization technique that finds the lowest point of a loss function. It is a technique that finds the slope of the loss function, moves it to a lower slope, and repeats the process until it reaches the lowest point. Here, the loss function is a function that defines the difference (i.e., error) between the result calculated by the output layer 130 and the actual value. The loss function may be Mean Squared Error (MSE) or Cross Entropy Error (CEE), but is not necessarily limited thereto.

FIG. 2A is a diagram showing the basic structure of a convolutional neural network (CNN) related to the present invention, and FIG. 2B is a diagram referenced to explain the learning process of the convolutional neural network shown in FIG. 2A.

Referring to FIGS. 2A and 2B, a convolutional neural network (CNN) 200 related to the present invention includes an input layer (210), one or more convolution layers (220), and one or more pooling layers. (pooling layer, 230), fully connected layer (240), and output layer (output layer, 250). Here, the pooling layer 230 may be included in the convolution layer 220.

The convolutional neural network 200 consists of a part that extracts features of input data and a part that classifies classes of input data. Here, the feature extraction part consists of an input layer 210, a convolutional layer 220, and a polling layer 230, and the class classification part consists of a fully connected layer 240 and an output layer 250.

The input layer 210 refers to a layer into which learning data, that is, training data and test data, are input. Typically, learning data used in a convolutional neural network (CNN) may be multidimensional data such as image data or a matrix.

The convolution layer 220 serves to extract features of the input data through a convolution operation between the input data and a filter, which is a collection of weights. The convolution layer 220 consists of a filter that extracts features of input data and an activation function that converts a convolution operation value between the input data and the filter into a non-linear value. The activation function may be a ReLU (Rectified Linear Unit) function, but is not necessarily limited thereto.

The convolution layer 220 may output a plurality of feature maps through a convolution operation between input data and various filters. Thereafter, the convolution layer 220 may apply an activation function to a plurality of feature maps and output a plurality of activation maps.

The pooling layer (or sub-sampling layer, 230) receives the output data of the convolution layer 220 as input and plays the role of reducing the size of the output data (i.e., activation map) or emphasizing specific data. Pooling methods of the pooling layer 230 include Max Pooling, Average Pooling, and Min Pooling, and among them, Max Pooling is the most widely used.

The fully connected layer 240 plays the role of changing the data type of the convolutional neural network (CNN, 200) into a fully connected neural network. In other words, the fully connected layer 240 flattens the three-dimensional output value of the pooling layer 230 into a one-dimensional vector and connects it to all nodes of the output layer 250 like a general neural network connection.

The output layer 250 performs the role of classifying the classes of input data and outputting a result value. The output layer 250 normalizes the value received from the fully connected layer 240 to a value between 0 and 1, and may play the role of ensuring that the total of the output values is always 1. To this end, the output layer 250 may include an activation function such as softmax.

The learning operation of the convolutional neural network 200 having this structure is briefly explained as follows. First, set the initial values of the parameters Weight (W) and Bias (B) in each layer. Afterwards, the net input function value in each layer is calculated for one learning (training) data, and finally the output value (i.e., result value) by the activation function is calculated. Here, the net input function value refers to the value input to the activation function of each layer. Next, the weights and biases in each layer are updated so that the difference between the output value by the activation function of the output layer and the actual value is within the tolerance range. Finally, for all learning data, learning is terminated when the difference between the output value by the activation function of the output layer and the actual value is within the tolerance range.

That is, as shown in FIG. 2B, the learning process of the convolutional neural network 200 can be defined as a repetitive process of feedforward (FF) and backpropagation (BP). This repetitive process may continue until the error in the output layer 250 approaches 0.

FIG. 3 is a diagram illustrating types of quantum gates related to the present invention, and FIG. 4 is a diagram illustrating an example of a quantum circuit constructed using the quantum gates of FIG. 3.

Referring to Figures 3 and 4, the quantum circuit that makes up the quantum computer consists of several quantum gates. Unlike bits in conventional computers, qubits in quantum computers can have states that can be 0 and 1 at the same time, but as quantum computers must also be used for calculations, they must be in a specific state during calculations. For this, quantum computers require quantum gates.

Quantum gates are basically operated through matrix multiplication of complex vectors. This is because qubits, the quantum information unit of a quantum computer, are expressed as two-dimensional vectors.

Types of these quantum gates include NOT gate, Hadamard gate, Pauli XYZ gate, Phaseshift gate (S gate, T gate), CNOT gate, CZ gate, and SWAP gate.

The NOT gate is the same gate as the NOT gate among the logic gates of existing computers. It is a gate that changes the state of a qubit to 1 if it is 0 and to 0 if it is 1.

The Hadamard gate is a gate that puts qubits in the 0 or 1 state into a superposed state (0 and 1 exist at the same time). If the Hadamard gate is expressed as a matrix, it is expressed as the determinant in the drawing.

There are three types of Pauli gates: X, Y, and Z. This means that each qubit is rotated around the X, Y, and Z axes. If each gate is expressed as a matrix, it is expressed as the determinant in the drawing.

Phaseshift gate is a gate that changes the phase of a qubit. Types of the phaseshift gate include S gate and T gate, and the format for each is as shown in the drawing.

CNOT gate and CZ gate are gates in quantum computers that allow you to see the entanglement state in which one qubit affects another qubit. The CNOT gate is a gate that performs the NOT gate operation on the second qubit when the first qubit is 1, and the CZ gate performs the Pauli-Z gate operation on the second qubit when the first qubit is 1. It is a gate that does.

A SWAP gate is a gate that switches the states of two qubits in a quantum computer.　If the SWAP gate is expressed as a matrix, it is expressed as the determinant in the drawing.

By combining a plurality of such quantum gates, various quantum circuits can be formed. For example, as shown in FIG. 4, the quantum circuit 300 can be formed by sequentially connecting the first Hadamard gate 310, the CNOT gate 330, and the third Hadamard gate 320.

Figure 5 is a diagram schematically showing the structure of a quantum circuit related to the present invention. As shown in FIG. 5, the quantum circuits 400 and 500 related to the present invention may be composed of a combination of unitaries U ₁ to U _j respectively corresponding to one or more quantum gates. Here, an ideal quantum gate (i.e., a quantum gate without errors) can be expressed as U, and a practical quantum gate (i.e., a quantum gate with errors) can be expressed as U. It can be expressed as

The input state of the quantum circuits 400 and 500 is a density matrix. It can be defined as , the output state can be defined as j, and the space between the input and output of the corresponding quantum circuits (400, 500) is defined as a combination of unitaries corresponding to quantum gates. It can be.

Measurement outcome probability without error, which represents the result of measuring the output of the ideal quantum circuit 400. ) can be defined as Equation 1 below.

here, is the input state of the quantum circuit, U is the ideal unitary transform, is a measurement operator.

Meanwhile, the output outcome probability with error (measurement outcome probability with error) represents the result value of measuring the output of the actual quantum circuit 500. ) can be defined as Equation 2 below.

here, is the input state of the quantum circuit, is a practical quantum process, is a measurement operator.

The error existing in the practical quantum circuit 500 is the probability of the first measurement result of the practical quantum circuit 500 ( ) and the second measurement result probability of the ideal quantum circuit 400 ( ) can be quantified based on In other words, the error value of the quantum circuit ( ) can be calculated as in Equation 3 below.

As such, since each quantum gate has its own error, an error that is the accumulation of the errors of each quantum gate exists in a quantum circuit composed of a plurality of quantum gates. Additionally, the error that exists in a quantum circuit depends not only on the configuration of the quantum gates but also on the order of combination of the quantum gates. Therefore, it is necessary to correct errors existing in the quantum circuit by considering the configuration and combination order of the quantum gates. Hereinafter, in this specification, a method for effectively correcting errors existing in a quantum circuit using a pre-trained deep learning model will be described in detail.

Figure 6 is a flowchart explaining a quantum circuit error correction method according to an embodiment of the present invention.

Referring to FIG. 6, a quantum circuit error correction device according to an embodiment of the present invention is installed inside a quantum computer and can perform an operation to correct errors in quantum circuits constituting the quantum computer.

More specifically, the quantum circuit error correction device can check whether a command requesting error correction of the quantum circuits constituting the quantum computer is received from the user, etc. (S610).

As a result of the confirmation in step 610, if a command requesting quantum circuit error correction is received from the user, etc., the quantum circuit error correction device will Can be detected (S620). Here, the quantum circuit to be corrected may be at least one of a plurality of quantum circuits constituting a quantum computer. Meanwhile, depending on the embodiment, step 610 described above may be configured to be omitted.

Afterwards, the quantum circuit error correction device can call the deep learning model learned in advance (S630). At this time, the deep learning model may be a DNN model or a hybrid CNN model, but is not necessarily limited thereto.

The quantum circuit error correction device can detect input data of a deep learning model corresponding to the quantum circuit to be corrected. The input data includes information on the number of 1-qubit gates constituting the corresponding quantum circuit, information on the number of 2-qubit gates constituting the corresponding quantum circuit, error information of the corresponding quantum circuit, measurement result probability information of the corresponding quantum circuit, etc. can do.

The quantum circuit error correction device uses an error correction value (or error correction matrix, ) can be inferred (S640). In other words, the quantum circuit error correction device inputs the detected input data into a pre-trained deep learning model to create an error correction value ( ) can be inferred.

The quantum circuit error correction device uses the error correction value ( ) can be used to correct errors existing in the quantum circuit (S650). In other words, the quantum circuit error correction device measures the output of the actual quantum circuit ( ) to the error correction value ( ) can be subtracted to correct the error existing in the quantum circuit.

As described above, the quantum circuit error correction method according to an embodiment of the present invention easily corrects the error existing in the quantum circuit using a pre-learned deep learning model, using quantum gates for correcting the quantum circuit error. Not only does it not need to be added separately, but the calculation process for quantum circuit error correction is simple, saving time and energy required to correct errors existing in the quantum circuit. As the deep learning model, a deep neural network (DNN) model or a hybrid convolutional neural network (H-CNN) model may be used. First, we will explain in detail how to correct errors in quantum circuits using a deep neural network (DNN) model.

Figure 7 is a diagram showing the structure of a DNN model according to an embodiment of the present invention.

Referring to FIG. 7, the DNN model 700 according to an embodiment of the present invention is a learning model for correcting quantum circuit errors of an N qubit system, and includes one input layer (710) and two It may include two hidden layers (720, 730) and one output layer (740).

Data input to a plurality of nodes present in the input layer 710 of the DNN model 700 includes 1-qubit gate number information (G ₁ (a:b)) constituting the quantum circuit, 2-qubit gate number information (G ₂ (a:b)), error information of quantum circuit ( ), quantum circuit measurement result probability information ( ) may include. Here, a and b represent the depth of the quantum circuit. Therefore, G ₁ (a:b) refers to the number of 1-qubit gates of quantum gates located between depth a and depth b of the quantum circuit, and G ₂ (a:b) refers to the number of 1-qubit gates between depth a and depth b of the quantum circuit. It refers to the number of 2-qubit gates of quantum gates located between b.

For example, as shown in FIG. 9, the quantum circuit 900, which is the learning target or correction target of the DNN model 700, includes a plurality of unitaries (U ₁ to U _K ) corresponding to a plurality of quantum gates. It can be expressed as a combination. In this quantum circuit structure, the number information (G ₁ ) of 1-qubit gates input to the input layer 710 of the DNN model 700 is [G ₁₁ ?? G _1N ], and the number information (G ₂ ) of 2-qubit gates is [G ₂₁ ?? G _2N ] can be expressed. And, the error information of the quantum circuit input to the input layer 710 of the DNN model 700 ( ) can be defined as the error of the unitary (U _a ) located at the depth a of the quantum circuit, and the probability information of the measurement result of the quantum circuit ( ) can be defined as the probability of the measurement result of the unitary (U _b ) located at depth b of the quantum circuit.

The input layer 710 of the DNN model 700 may include a total of 2N+2 ^N+1 (=N+N+2 ^N +2 ^N ) nodes. Here, N nodes are nodes for inputting the number of 1-qubit gates, N nodes are nodes for inputting the number of 2-qubit gates, and 2 ^N nodes are nodes for inputting the error of the quantum circuit ( ) are the nodes for inputting, and the 2 ^N nodes represent the probability of the measurement result of the quantum circuit ( ) are the nodes for inputting.

Data output through a plurality of nodes present in the output layer 740 of the DNN model 700 contains an error correction value (or error correction value) to reduce (or alleviate) the error present in the quantum circuit. ) may include. The output layer 740 may include 2 ^N nodes.

Data input to a plurality of nodes present in the output layer 740 of the DNN model 700 is error information of the quantum circuit ( ) may include. Here, the error information ( ) can be defined as the error of the unitary (U _b ) located at depth b of the quantum circuit. And, the error information ( ) can be used to calculate a loss function in the learning process of the model 700.

Data input to the DNN model 700 can be set as independent variables of the model, and data output from the DNN model 700 can be set as dependent variables of the model.

Parameters used for nodes present in the hidden layers 720 and 730 of the DNN model 700 may include weight and bias. Additionally, the activation function used for the nodes existing in the hidden layers 720 and 730 of the DNN model 700 may be a sigmoid function, but is not necessarily limited thereto. Therefore, depending on the embodiment, a ReLU function, a softmax function, or an identity function may be used instead of the sigmoid function.

The loss function (E _RMS ) of the DNN model 700 can be defined as Equation 4 below.

here, is the actual error value of the quantum circuit ( ) to the error correction value (i.e., the error estimate value, ), which represents the final error value of the quantum circuit, and the value can be defined as Equation 5 below.

The DNN model 700 goes through a learning process to update the weights and biases of the nodes present in the hidden layers 720 and 730 using an optimization technique that finds the lowest point of the loss function. . At this time, gradient descent may be typically used as the optimization technique, but is not necessarily limited thereto.

In other words, the DNN model 700 aims to find an error correction value that minimizes the loss function. Therefore, the objective function (F) of the DNN model 700 can be defined as Equation 6 below.

Meanwhile, in this embodiment, the DNN model 700 is illustrated as having two hidden layers 720 and 730, but is not necessarily limited thereto, and may have fewer or more hidden layers. It will be obvious to those skilled in the art that this can be done.

Figure 8 is a diagram showing the structure of a DNN model according to another embodiment of the present invention.

Referring to FIG. 8, the DNN model 800 according to another embodiment of the present invention is a learning model for correcting quantum circuit errors of an N qubit system, and includes one input layer (810) and three It may include two hidden layers (820, 830, 840) and one output layer (830).

The DNN model 800 according to the present invention, unlike the DNN model 700 of FIG. 7 described above, may further include one hidden layer 820. That is, the DNN model 800 may further include a hidden layer 820 that performs batch normalization (BN) only on nodes connected to specific input data. Here, the batch normalization (BN) means normalizing using the mean and variance for each batch even if the data has various distributions for each batch unit during the learning process.

Among the data input to the input layer 810 of the DNN model 800, the number of gates of the quantum circuit has an integer value, while the error value of the quantum circuit ( ) and measurement result probability ( ) has a value between 0 and 1. Therefore, by performing batch normalization on the nodes of the first hidden layer 820 connected to the input data (G ₁ (a:b), G ₂ (a:b)) having integer values, the first hidden layer ( The input data distribution of the second hidden layer 830 connected to 820) may be equalized to a value between 0 and 1.

Machine learning can be performed on the DNN models 700 and 800 with this structure. More specifically, a learning target quantum circuit belonging to a predetermined learning set can be selected, and quantum gates constituting the selected learning target quantum circuit can be analyzed to detect data to be input to the DNN model. At this time, the data to be input to the DNN model includes 1-qubit gate number information (G ₁ (a:b)), 2-qubit gate number information (G ₂ (a:b)), and error information of the quantum circuit to be learned. information( ) and measurement result probability information ( ) may include.

Once detection of the input data is completed, the detected input data can be input into the DNN model to train the corresponding DNN model. At this time, the corresponding DNN model can be trained repeatedly by sequentially changing the variables (a, b, i) of the detected input data.

Once learning of the corresponding quantum circuit is completed, the same learning process can be performed by sequentially selecting other quantum circuits belonging to the predetermined learning set. This learning process can be performed repeatedly for all quantum circuits included in the learning set.

Figure 10 is a diagram referenced to explain the process of selecting a learning target quantum circuit and learning a DNN model based on the selected learning target quantum circuit. As shown in FIG. 10, quantum circuits to be learned can be selected, and a DNN model for correcting (alleviating) quantum circuit errors can be trained based on the selected quantum circuits to be learned. At this time, the quantum circuits to be learned may be quantum circuits having quantum gates less than a predetermined first number. For example, the quantum circuits to be learned may be quantum circuits having 10 or less quantum gates.

FIG. 11 is a diagram referenced to explain the types of quantum circuits to be corrected and the process of correcting errors in the quantum circuits to be corrected using a previously learned DNN model. As shown in FIG. 11, a quantum circuit to be corrected (or a quantum circuit to be estimated) is selected, the selected quantum circuit is input into a pre-trained DNN model to infer the error correction value of the quantum circuit, and the inferred Errors in the quantum circuit can be corrected based on the error correction value.

The quantum circuits to be corrected are quantum circuits (U ₁ to U _k ) that have the same quantum gate configuration as the quantum gate configurations of the learning target quantum circuits, and have a greater number of quantum gate configurations than the quantum gate configurations of the learning target quantum circuits. It may include quantum circuits (U ₁ to U _k+l ) and quantum circuits (V ₁ to V _j ) having quantum gate configurations different from the quantum gate configurations of the quantum circuits to be learned. At this time, the quantum circuits subject to correction may be quantum circuits having quantum gates less than or equal to a predetermined second number. For example, the quantum circuits subject to correction may be quantum circuits having 20 or less quantum gates.

In this way, the present invention trains a DNN model based on quantum circuits with a quantum gate configuration with a relatively short depth, and applies a pre-trained DNN model to quantum circuits with a quantum gate configuration with a relatively long depth to determine quantum Errors in circuits are corrected.

Meanwhile, in the quantum circuit error correction method described above, the number of data input to the deep neural network (DNN) model is large, so the computational process for learning the DNN model is somewhat complicated. This problem can be solved through a quantum circuit error correction method using a hybrid CNN model. Below, a method for correcting errors in a quantum circuit using a hybrid CNN model will be described in detail.

FIGS. 12A and 12B are diagrams referenced to explain the structure of a hybrid CNN model and learning data input to the input layer and output layer of the model according to an embodiment of the present invention.

Referring to FIGS. 12A and 12B, the hybrid CNN model 1200 according to an embodiment of the present invention combines a deep neural network (DNN) algorithm with a convolutional neural network (CNN) algorithm to improve quantum circuit error correction performance. It's a model. The H-CNN model 1200 is a learning model for correcting quantum circuit errors of an N qubit system, and includes an input layer (1210), one or more hidden layers (1220), and an output layer (output layer, 1230). Here, the input layer 1230 may include one or more convolution layers, a pooling layer, and a fully connected layer to pre-process some of the input data.

Data input to a plurality of nodes present in the input layer 1210 of the H-CNN model 1200 is gate matrix information (G' _ij ) indicating the number of gates between qubit i and qubit j of the quantum circuit. , the first local error information of the quantum circuit ( ), second local error information of the quantum circuit ( ), target state information of the quantum circuit (t), target measurement result probability information of the quantum circuit ( ) may include. Here, a and b represent the depth of the quantum circuit.

For example, as shown in FIG. 12A, the quantum circuit 1300 that is the learning or correction target of the H-CNN model 1200 has a plurality of unitaries (U ₁ to U _K ) corresponding to a plurality of quantum gates. ) can be expressed as a combination of In this quantum circuit structure, the first local error information of the quantum circuit input to the input layer 1210 of the H-CNN model 1200 ( ) can be defined as the local error of the unitary (U _a ) located at the a-th depth, and the second local error information of the quantum circuit ( ) can be defined as the local error of the unitary (U _b ) located at the b-th depth. In addition, the target state information (t) of the quantum circuit can be defined as bit information representing one of the 2 ^N qubit states, and the target measurement result probability information of the quantum circuit ( ) can be defined as the probability of the measurement result of the target qubit state of the unitary (U _b ) located at the b-th depth.

The gate matrix (G' _{i, j} ) input to the input layer 1210 of the H-CNN model 1200 is a matrix representing the number of gates existing between qubit i and qubit j of the quantum circuit, N* It can be defined as an N matrix. Here, the gate matrix (G' _{i, j} ) may be pre-processed through one or more convolutional layers, a pooling layer, and a fully connected layer and then input to the input layer 1210. For example, as shown in FIG. 12B, the convolution layer generates a plurality of feature maps through a convolution operation between input data (i.e., G' _{i, j} ) and one or more filters, and the feature maps A plurality of activation maps can be created by applying an activation function to . Afterwards, the pooling layer can receive the output data of the convolution layer as input and reduce the size of the output data (i.e., activation map) or emphasize specific data. The fully connected layer can change the data type of the CNN algorithm to Fully Connected Neural Network. The output data of the complete connection layer may be input to the input layer 1210. In this way, the H-CNN model 1200 can extract the features of the gate matrix (G' _{i, j} ) using the CNN algorithm and then input the features into the input layer 1210.

The input layer 1210 of the H-CNN model 1200 may include a plurality of nodes. Here, N nodes contain the first local error information of the quantum circuit ( ) are the nodes for inputting, and the N nodes are the second local error information of the quantum circuit ( ) are nodes for inputting, N nodes are nodes for inputting target state information (t) of the quantum circuit, and one node is the target measurement result probability information of the quantum circuit ( ) is a node for inputting.

The H-CNN model 1200 provides error information of the quantum circuit (e.g., ) can be input to the input layer 1210 on a local basis. In other words, the H-CNN model 1200 can input error information of the quantum circuit in units of qubits. Accordingly, unlike the DNN model 700 described above, the H-CNN model 1200 can simplify the calculation process of the learning model by inputting only N pieces of data into the learning model.

The data output through the node present in the output layer 1240 of the H-CNN model 1200 contains an error correction value (or error correction value) to reduce (or alleviate) the error present in the quantum circuit. ) may include. The output layer 540 may include one node.

Data input to the node present in the output layer 1240 of the H-CNN model 1200 is the target error information of the quantum circuit ( ) may include. Here, the target error information ( ) can be defined as the error in the target qubit state of the unitary (U _b ) located at the b-th depth of the quantum circuit. The target error information ( ) can be used to calculate the loss function during the learning process of the model.

Data input to the H-CNN model 1200 can be set as independent variables of the model, and data output from the H-CNN model 1200 can be set as dependent variables of the model.

Parameters used for nodes existing in the hidden layer 1220 of the H-CNN model 1200 may include weight and bias. Additionally, the activation function used for nodes existing in the hidden layer 1220 of the H-CNN model 1200 may be a sigmoid function, but is not necessarily limited thereto.

The loss function (E _RMS ) of the H-CNN model 1200 can be defined as Equation 7 below.

here, is the actual error value of the quantum circuit ( ) to the error correction value ( ), which represents the final error value of the quantum circuit, and the corresponding value can be defined as Equation 8 below.

The H-CNN model 1200 goes through a learning process to update the weights and biases of nodes existing in the hidden layer 1220 using an optimization technique that finds the lowest point of the loss function. . At this time, gradient descent may be typically used as the optimization technique, but is not necessarily limited thereto.

Figure 13 is a diagram referenced to explain the process of selecting a learning target quantum circuit and learning an H-CNN model based on the selected learning target quantum circuit. As shown in FIG. 13, quantum circuits for learning can be selected, and an H-CNN model for correcting (relieving) quantum circuit errors can be trained based on the selected quantum circuits for learning. At this time, the quantum circuits to be studied may be quantum circuits having quantum gates of a predetermined number or less. For example, the quantum circuits to be studied may be quantum circuits having 10 or less quantum gates.

FIG. 14 is a diagram referenced to explain the types of quantum circuits to be corrected and the process of correcting errors in the quantum circuits to be corrected using a previously learned H-CNN model. As shown in FIG. 14, a quantum circuit to be corrected (or a quantum circuit to be inferred) is selected, and the selected quantum circuit is input into a pre-trained H-CNN model to infer the error correction value of the quantum circuit. The error of the quantum circuit can be corrected based on the inferred error correction value.

The quantum circuits to be corrected are quantum circuits (U ₁ to U _k ) that have the same quantum gate configuration as the quantum gate configurations of the learning target quantum circuits, and have a greater number of quantum gate configurations than the quantum gate configurations of the learning target quantum circuits. It may include quantum circuits (U ₁ to U _k+l ) and quantum circuits (V ₁ to V _j ) having quantum gate configurations different from the quantum gate configurations of the quantum circuits to be learned. At this time, the quantum circuits to be corrected may be quantum circuits having quantum gates less than a predetermined number. For example, the quantum circuits subject to correction may be quantum circuits having 20 or less quantum gates.

In this way, the present invention trains an H-CNN model based on quantum circuits with a quantum gate configuration with a relatively short depth, and a pre-trained H-CNN model for quantum circuits with a quantum gate configuration with a relatively long depth. is applied to correct errors in quantum circuits.

Figure 15 is a block diagram of a computing device according to an embodiment of the present invention.

Referring to FIG. 15, a computing device 1500 according to an embodiment of the present invention includes at least one processor 1510, a computer-readable storage medium 1520, and a communication bus 1530. The computing device 1500 may be the above-described quantum circuit error correction device or one or more components included in the quantum circuit error correction device.

The processor 1510 may enable the computing device 1500 to operate according to the above-mentioned exemplary embodiment. For example, the processor 1510 may execute one or more programs 1525 stored in the computer-readable storage medium 1520. The one or more programs may include one or more computer-executable instructions, which, when executed by the processor 1510, cause the computing device 1500 to perform operations according to example embodiments. It can be.

The computer-readable storage medium 1520 is configured to store computer-executable instructions or program code, program data, and/or other suitable forms of information. The program 1525 stored in the computer-readable storage medium 1520 includes a set of instructions executable by the processor 1510. In one embodiment, computer-readable storage medium 1520 includes memory (volatile memory, such as random access memory, non-volatile memory, or an appropriate combination thereof), one or more magnetic disk storage devices, optical disk storage devices, flash. It may be memory devices, another form of storage medium that can be accessed by computing device 1500 and store desired information, or a suitable combination thereof.

Communication bus 1530 interconnects various other components of computing device 1500, including processor 1510 and computer-readable storage medium 1520.

Computing device 1500 may also include one or more input/output interfaces 1540 and one or more network communication interfaces 1560 that provide an interface for one or more input/output devices 1550 . The input/output interface 1540 and the network communication interface 1560 are connected to the communication bus 1530.

Input/output device 1550 may be connected to other components of computing device 1500 through input/output interface 1540. Exemplary input/output devices 1550 include a pointing device (such as a mouse or trackpad), a keyboard, a touch input device (such as a touchpad or touch screen), a voice or sound input device, various types of sensor devices, and/or an imaging device. It may include input devices and/or output devices such as display devices, printers, speakers, and/or network cards. The exemplary input/output device 1550 may be included within the computing device 1500 as a component constituting the computing device 1500, or may be connected to the computing device 1500 as a separate device distinct from the computing device 1500. It may be possible.

The above-described present invention can be implemented as computer-readable code on a program-recorded medium. Computer-readable media includes all types of recording devices that store data that can be read by a computer system. Examples of computer-readable media include HDD (Hard Disk Drive), SSD (Solid State Disk), SDD (Silicon Disk Drive), ROM, RAM, CD-ROM, magnetic tape, floppy disk, optical data storage device, etc. There is. Accordingly, the above detailed description should not be construed as restrictive in all respects and should be considered illustrative. The scope of the present invention should be determined by reasonable interpretation of the appended claims, and all changes within the equivalent scope of the present invention are included in the scope of the present invention.

700: DNN model 1200: H-CNN model
710/1210: input layer 720/730/1220: hidden layer
740/1230: Output layer 1500: Computing device
1510: Processor 1520: Computer-readable storage medium
1530: Communication Bus

Claims (15)

In a quantum circuit error correction method in a quantum computer,
Detecting a quantum circuit to be corrected among a plurality of quantum circuits constituting the quantum computer;
calling a pre-trained deep learning model to correct errors in the plurality of quantum circuits;
inferring an error correction value of the detected quantum circuit using the called deep learning model; and
Comprising the step of correcting the error of the detected quantum circuit based on the inferred error correction value,
If the deep learning model is a deep neural network (DNN) model,
The independent variable of the DNN model is information on the number of 1-qubit gates (G ₁ (a:b)) of unitaries located between depth a and depth b of the quantum circuit, between depth a and depth b of the quantum circuit. Information on the number of 2-qubit gates of unitaries located in (G ₂ (a:b)), error information of unitaries located at depth a of the quantum circuit ( ) and probability information of the measurement result of the unitary located at depth b of the quantum circuit ( ) Contains at least one of,
The correction step is a quantum circuit error correction method characterized in that the error existing in the quantum circuit is corrected by subtracting the inferred error correction value from the result of measuring the actual output of the detected quantum circuit. According to paragraph 1,
A quantum circuit error correction method further comprising detecting input data of a deep learning model corresponding to the detected quantum circuit. The method of claim 2, wherein the inference step is,
A quantum circuit error correction method, characterized in that the error correction value is inferred by inputting the detected input data into the deep learning model. delete According to paragraph 1,
A quantum circuit error correction method, wherein each quantum circuit is composed of a combination of a plurality of unitaries corresponding to a plurality of quantum gates. delete delete According to paragraph 1,
The dependent variable of the DNN model is the error correction information of the unitary located at depth b of the quantum circuit ( ) Quantum circuit error correction method comprising: According to clause 8,
Error information of the unitary located at depth b of the quantum circuit ( ) is a quantum circuit error correction method, characterized in that it is used to calculate a loss function in the learning process of the DNN model. In a quantum circuit error correction method in a quantum computer,
Detecting a quantum circuit to be corrected among a plurality of quantum circuits constituting the quantum computer;
calling a pre-trained deep learning model to correct errors in the plurality of quantum circuits;
inferring an error correction value of the detected quantum circuit using the called deep learning model; and
Comprising the step of correcting the error of the detected quantum circuit based on the inferred error correction value,
If the deep learning model is a Hybrid Convolutional Neural Network (H-CNN) model,
The independent variables of the H-CNN model are gate matrix information (G' _ij ) indicating the number of gates between qubit i and qubit j of the quantum circuit, and the first local error of the unitary located at depth a of the quantum circuit. information( ), the second local error information of the unitary located at depth b of the quantum circuit ( ), target state information of the quantum circuit (t), target measurement result probability information of the unitary located at depth b of the quantum circuit ( ) and includes at least one of
The correction step is a quantum circuit error correction method characterized in that the error existing in the quantum circuit is corrected by subtracting the inferred error correction value from the result of measuring the actual output of the detected quantum circuit. According to clause 10,
In the learning process of the H-CNN model, the gate matrix information (G' _ij ) is pre-processed through one or more convolution layers, pooling layers, and fully connected layers and input to the input layer of the H-CNN model. Quantum circuit error correction method. According to clause 10,
The dependent variable of the H-CNN model is the target error information of the unitary located at depth b of the quantum circuit ( ) Quantum circuit error correction method comprising: According to clause 12,
Target error information of the unitary located at depth b of the quantum circuit ( ) is a quantum circuit error correction method, characterized in that it is used to calculate a loss function in the learning process of the H-CNN model. A computer program stored in a computer-readable recording medium so that the method according to any one of claims 1 to 3, 5, and 8 to 13 can be executed on a computer. A memory that stores a deep learning model learned in advance for error correction of a plurality of quantum circuits constituting a quantum computer; and
Detecting a quantum circuit to be corrected among the plurality of quantum circuits, inferring an error correction value of the detected quantum circuit using a deep learning model stored in the memory, and detecting the error correction value based on the inferred error correction value. Includes a processor that corrects errors in the quantum circuit,
The processor corrects errors existing in the quantum circuit by subtracting the inferred error correction value from the result of measuring the actual output of the detected quantum circuit,
If the deep learning model is a deep neural network (DNN) model,
The independent variable of the DNN model is information on the number of 1-qubit gates (G ₁ (a:b)) of unitaries located between depth a and depth b of the quantum circuit, between depth a and depth b of the quantum circuit. Information on the number of 2-qubit gates of unitaries located in (G ₂ (a:b)), error information of unitaries located at depth a of the quantum circuit ( ) and probability information of the measurement result of the unitary located at depth b of the quantum circuit ( ) A quantum circuit error correction device comprising at least one of the following:

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